--- title: "Visualization and Growth Curve modeling of CensusSeq iPSC lines" format: html: theme: - default page-layout: full code-fold: true code-tools: true toc: true number-sections: true embed-resources: true jupyter: python3 ---

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from scipy.ndimage import gaussian_filter1d
import seaborn as sns
import matplotlib as mpl
from matplotlib.lines import Line2D
import yaml
from scipy import stats

import sys
sys.path.append('../resources/')
from ImagingUtilities import *

import warnings
warnings.filterwarnings('ignore')

from scipy.optimize import curve_fit
from sklearn.preprocessing import StandardScaler

from sklearn.metrics import mean_squared_log_error, r2_score

with open("../data/resources/rcParams.yaml") as f:
    rcParamsDict = yaml.full_load(f)
    for k in rcParamsDict["rcParams"]:
        print("{} {}".format(k,rcParamsDict["rcParams"][k]))
        plt.rcParams[k] = rcParamsDict["rcParams"][k]
    for k1 in set(list(rcParamsDict)).difference(set(["rcParams"])):
        print("{} {}".format(k1,rcParamsDict[k1]))

figure.dpi 80
savefig.dpi 500
figure.figsize [10, 10]
axes.facecolor None
figure.facecolor None
dotSize 20

line_palette = {
 'CTL01A': '#DBB807',
    'CTL08A': '#0FB248',
    'CTL04E': '#FF0054',
    'CTL02A': '#7B00FF',
'H9': '#72190E',
 'H1': '#994F88',
 'CTL05A': '#1965B0',
 'CTL07C': '#437DBF',
 'CTL06F': '#CAE0AB',
 'CTL09A': '#FFFF00',
 'KTD8.2': '#E65518',
 'UCSFi001-A': '#7BAFDE'}

Load data

total_df = pd.read_csv('../../iPSC_imaging/quantifications/quantification.csv', index_col=0)
add_tp = pd.read_csv('../../iPSC_imaging/quantifications/quantification_addTP.csv', index_col=0)
total_df[ ~ total_df.duplicated()]
total_df = pd.concat([total_df, add_tp])

donor_map_names = {i:j for i, j in zip(total_df['line'], total_df['line'])}
donor_map_names['CHD2WT'] = 'UCSFi001-A'
donor_map_names['CHD8WT'] = 'H9'
total_df['line'] = total_df['line'].map(donor_map_names)
total_df.shape

(2776, 16)

total_df['pixel_size'] = 1.38

total_df['Area (microm2)'] = total_df.total_area * 1.38
total_df['Area (mm2)'] = total_df['Area (microm2)'] / 1000

total_df['line'].unique()

array(['H1', 'CTL04E', 'CTL02A', 'CTL05A', 'H9', 'KTD8.2', 'CTL09A',
       'CTL06F', 'CTL08A', 'CTL07C', 'UCSFi001-A', 'CTL01A'], dtype=object)

all_tp = total_df.time_point.unique()
all_tp.sort()
all_tp

array(['01_11_23_t18', '02_11_23_t18', '02_11_23_t9', '03_11_23_t18',
       '03_11_23_t9', '04_11_23_t10', '04_11_23_t18', '05_11_23_t18',
       '05_11_23_t9', '06_11_23_t18', '06_11_23_t9', '07_11_23_t18',
       '07_11_23_t9', '08_11_23_t18', '08_11_23_t9', '09_11_23_t20',
       '09_11_23_t9', '10_11_23_t18', '10_11_23_t9', '11_11_23_t18',
       '11_11_23_t9', '12_11_23_t13', '12_11_23_t18', '13_11_23_t18',
       '13_11_23_t9', '14_11_23_t17', '14_11_23_t9', '15_11_23_t17',
       '15_11_23_t9', '16_11_23_t10', '16_11_23_t18', '17_11_23_t17',
       '17_11_23_t9', '18_11_23_t10', '18_11_23_t18', '19_11_23_t10',
       '19_11_23_t18', '20_11_23_t18', '20_11_23_t9', '21_11_23_t17',
       '21_11_23_t9', '22_11_23_t10', '31_10_23_t18', '31_10_23_t9'],
      dtype=object)

Here I'm adding a few quantifications:

1. norm_factor: the normalization factor, corresponding to the mean area of the area percentage of all lines for each time point post split (called split_time)
2. perc_area_norm: the normalized percentage area, corresponding to the percentage area divided by the the normalization factor (1.)
3. mean_area_tp: the mean area of each line at each time point post split (called split_time)
4. area_error: the percentage "error" of the total area computed with respect to the mean of that line at that time point
5. std: the standard deviation of each area with respect to (3.)
6. cv: the coefficient of variation, corresponding to the ratio between the standard deviation and the mean

total_df['line_split'] = total_df['line'].astype('str') + '_' + total_df['split_time'].astype('str')

mean_df_time_point = total_df.groupby(['split_time']).mean('perc_area')
mean_df_time_point_dict = {i:j for i, j in zip(mean_df_time_point.index, mean_df_time_point.perc_area)}
mean_df_time_point_dict

area_df_time_point = total_df.groupby(['line','split_time']).mean('Area (microm2)').reset_index()
area_df_time_point['line_split'] = area_df_time_point['line'].astype('str') + '_' + area_df_time_point['split_time'].astype('str')
area_df_time_point = {i:j for i, j in zip(area_df_time_point.line_split, area_df_time_point['Area (microm2)'])}
area_df_time_point

total_df['norm_factor'] = total_df.split_time.map(mean_df_time_point_dict)
total_df['perc_area_norm'] = total_df['perc_area'] / total_df['norm_factor']

total_df['mean_area_tp'] = total_df.line_split.map(area_df_time_point)
total_df['area_error'] = (total_df['mean_area_tp'] - total_df['Area (microm2)']) / total_df['Area (microm2)']
total_df['std'] = np.sqrt((total_df['Area (microm2)'] - total_df['mean_area_tp'])**2 / len(total_df))
total_df['cv'] = total_df['std'] / total_df['mean_area_tp']

total_df['line_n_split'] = total_df['line'] + '_' + total_df['n_split'].astype('str')

total_df['norm_factor_t0'] = total_df['line_n_split'].map(norm_area_dict) total_df['norm_area_t0'] = total_df['Area (microm2)'] / total_df['norm_factor_t0']

sns.kdeplot(total_df['cv'])

<Axes: xlabel='cv', ylabel='Density'>

ax = sns.kdeplot(total_df['area_error'])
ax.axvline(15)

<matplotlib.lines.Line2D at 0x7f6c32443160>

ax = sns.kdeplot(total_df['area_error'])
ax.set_xlim(-1, 30)
ax.axvline(10)

<matplotlib.lines.Line2D at 0x7f6c3250f340>

fig, ax = plt.subplots(figsize = (20, 10))
sns.scatterplot(data = total_df, y = 'perc_area', x = 'split_time', ax = ax, hue = 'line', palette=line_palette)

<Axes: xlabel='split_time', ylabel='perc_area'>

total_df = total_df[~((total_df['split_time'] < 25) & (total_df['perc_area'] > 10))]

ax = sns.kdeplot(np.log10(total_df['area_error']))

total_df = total_df[total_df['area_error'] < 5]
total_df.shape

(2170, 25)

idx_max = total_df.groupby('line')['n_split'].idxmax()

# Filter the DataFrame using these indices
filtered_df = total_df.drop(idx_max)
filtered_df

	total_area	perc_area	mean_area_per_colony	n_colonies	time_point	confluency/generation	hour	month	day	line	...	split_time	pixel_size	Area (microm2)	Area (mm2)	line_split	mean_area_tp	area_error	std	cv	line_n_split
CTL04E_3_14_11_1.czi	2532723.0	26.606326	1.266362e+06	2.0	14_11_23_t9	generation	9	11	14	CTL04E	...	159.0	1.38	3495157.74	3495.15774	CTL04E_159.0	3.497834e+06	0.000766	50.791607	0.000015	CTL04E_3
CTL02A_3_14_11_3.czi	1051145.0	11.042308	1.313931e+05	8.0	14_11_23_t9	generation	9	11	14	CTL02A	...	44.0	1.38	1450580.10	1450.58010	CTL02A_44.0	1.548576e+06	0.067556	1859.928320	0.001201	CTL02A_3
CHD8WT_3_14_11_1.czi	1655866.0	17.394919	1.655866e+05	10.0	14_11_23_t9	generation	9	11	14	H9	...	44.0	1.38	2285095.08	2285.09508	H9_44.0	9.615470e+05	-0.579209	25120.598728	0.026125	H9_3
KTD8.2_3_14_11_4.czi	862216.0	9.057603	2.874053e+05	3.0	14_11_23_t9	generation	9	11	14	KTD8.2	...	72.0	1.38	1189858.08	1189.85808	KTD8.2_72.0	7.105711e+05	-0.402810	9096.742330	0.012802	KTD8.2_3
CTL09A_4_14_11_5.czi	165602.0	1.739654	2.760033e+04	6.0	14_11_23_t9	generation	9	11	14	CTL09A	...	24.0	1.38	228530.76	228.53076	CTL09A_24.0	2.885001e+05	0.262413	1138.202417	0.003945	CTL09A_4
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
CTL08A_5_22_11_2.czi	946317.0	9.941087	6.759407e+04	14.0	22_11_23_t10	generation	10	11	22	CTL08A	...	17.0	1.38	1305917.46	1305.91746	CTL08A_17.0	1.797598e+06	0.376502	9331.962580	0.005191	CTL08A_5
CTL08A_5_22_11_3.czi	638843.0	6.711064	1.064738e+05	6.0	22_11_23_t10	generation	10	11	22	CTL08A	...	17.0	1.38	881603.34	881.60334	CTL08A_17.0	1.797598e+06	1.039010	17385.334447	0.009671	CTL08A_5
CTL01A_5_22_11_4.czi	834622.0	8.767728	5.961586e+04	14.0	22_11_23_t10	generation	10	11	22	CTL01A	...	17.0	1.38	1151778.36	1151.77836	CTL01A_17.0	1.359752e+06	0.180567	3947.276901	0.002903	CTL01A_5
CTL08A_5_22_11_4.czi	857634.0	9.009469	1.072042e+05	8.0	22_11_23_t10	generation	10	11	22	CTL08A	...	17.0	1.38	1183534.92	1183.53492	CTL08A_17.0	1.797598e+06	0.518838	11654.751425	0.006484	CTL08A_5
CHD8WT_5_22_11_1.czi	245495.0	2.578932	1.227475e+05	2.0	22_11_23_t10	generation	10	11	22	H9	...	17.0	1.38	338783.10	338.78310	H9_17.0	1.725624e+06	4.093595	26321.881011	0.015254	H9_5

2151 rows × 25 columns

total_df['logArea'] = np.log10(total_df['Area (microm2)'] + 0.000001)

Growth curves total area - by line

Here we fitted a polynomial regression function of order 3 (exploratory to look at what type of shapes we expect from the curves):

order = total_df.line.unique().tolist()
order.sort()

sns.set_theme(style="ticks")

# Initialize a grid of plots with an Axes for each walk
grid = sns.FacetGrid(total_df.sort_values(by = 'split_time'), col="line", hue = 'line', palette=line_palette,
                     col_wrap=4, height=5, col_order = order)


# Draw a line plot to show the trajectory of each random walk
grid.map(sns.regplot, "split_time", "Area (mm2)", order = 3)

grid.set_axis_labels("Time point post split", "Area (mm2)")

# Adjust the arrangement of the plots
grid.fig.tight_layout(w_pad=1)

Without fitting any regression (line goes through the mean and the highligthed data around is the standard deviation):

sns.set_theme(style="ticks")

# Initialize a grid of plots with an Axes for each walk
grid = sns.FacetGrid(total_df.sort_values(by = 'split_time'), col="line", hue = 'line', palette=line_palette,
                     col_wrap=4, height=5, col_order = order)

# Draw a line plot to show the trajectory of each random walk
grid.map(sns.lineplot, "split_time", "Area (mm2)", markers = True)

grid.set_axis_labels("Time point post split", "Total Area (pixels)")

# Adjust the arrangement of the plots
grid.fig.tight_layout(w_pad=1)

We use the area then average all the FOV for a specific time points in each line. The plot is composed by:

• a solid blue line, that is the smoothed version of this growth curve (using the function gaussian_filter1d from numpy),
• the red around that it is the standard deviation
• the dotted grey line that is the original signal

fig, ax = plt.subplots(4, 3, figsize=(30, 21), gridspec_kw={'hspace': 0.7})
ax = ax.flatten()

for ax_index, line in enumerate(total_df.line.unique()):
    sub = total_df[(total_df.line == line) & (total_df.n_split != 'day')].sort_values(by='datetime')
    mean_st = sub.groupby('split_time')['Area (mm2)'].mean()
    std_st = sub.groupby('split_time')['Area (mm2)'].std()
    y_pos = mean_st.index
    ydata = sub['Area (microm2)'].values
    xdata = sub.split_time.values.astype('int')
    farray = mean_st.values

    # Smoothing
    farray_smooth = gaussian_filter1d(farray, sigma=3)

    # Error formatting
    upper_err = gaussian_filter1d(farray + (std_st / 2).values, sigma=3)
    lower_err = gaussian_filter1d(farray - (std_st / 2).values, sigma=3)

    ax[ax_index].scatter(xdata, ydata)
    ax[ax_index].plot(y_pos, farray, '--', linewidth=0.7, color='k', alpha=0.45)
    ax[ax_index].plot(y_pos, farray_smooth, color='#2374AB')
    ax[ax_index].fill_between(y_pos, upper_err, lower_err, color='crimson', alpha=0.2)

    # Use meaningful limits for better visualization
    ax[ax_index].set_ylim(0, np.max(farray) * 1.25)

    # Rotate x-axis labels for better readability
    ax[ax_index].tick_params(axis='x', rotation=90)

    # Set axis labels and title
    ax[ax_index].set_title(f'Line {line}')
    ax[ax_index].set_ylabel('Total area')
    ax[ax_index].set_xlabel('Time point after split')

plt.tight_layout()  # Adjust layout to prevent overlapping
plt.show()

Growth curves total area - by line and split

Here we fitted a polynomial regression function of order 3:

sns.set_theme(style="ticks")

split_palette = {'1': '#264653', '2': '#2a9d8f', '3': '#8ab17d', '4': '#e9c46a', '5': '#f4a261', '6': '#e76f51'}
line_split_palette = {}

for i in total_df.line_n_split.unique():
    split_n = i.split('_')[-1]
    line_split_palette[i] = split_palette[split_n]

custom_handles = [Line2D([0], [0], color=color, lw=2) for color in split_palette.values()]
grid = sns.FacetGrid(total_df.sort_values(by = 'split_time'), col="line", hue = 'line_n_split', palette=line_split_palette,
                     col_wrap=4, height=5, col_order = order)
grid.map(sns.lineplot, "split_time", "Area (mm2)", markers = True)

grid.add_legend()
if grid._legend:
    grid._legend.remove()  

legend = grid.fig.legend(custom_handles, split_palette.keys(), ncol=2, frameon=False, bbox_to_anchor = (1.2,1), fontsize = 25)

legend.set_title('Passage number', prop={'size': 30})

for ax in grid.axes.flat:
    ax.set_title(ax.get_title(), fontsize=35)

# Increase the size of x and y tick labels
for ax in grid.axes.flat:
    ax.tick_params(axis='x', labelsize=20)
    ax.tick_params(axis='y', labelsize=20)

grid.set_axis_labels("Hours after splitting", "Total area (mm2)", fontsize = 25)
grid.fig.tight_layout(w_pad=1)
grid.fig.savefig('./figures/raw_GC_iPSC_dividedSplit.svg', dpi = 300, bbox_inches = 'tight')

I need to filter out the combination of "line" - "number of split" that do not have enough data point to fit an order 3 polynomial regression:

sns.set_theme(style="ticks")

boolean_sel = pd.Series(total_df.groupby(['line_n_split'])['split_time'].count() > 5)
boolean_sel = boolean_sel[boolean_sel]
filtered_total = total_df[total_df.line_n_split.isin(boolean_sel.index)]

# Initialize a grid of plots with an Axes for each walk
grid = sns.FacetGrid(filtered_total.sort_values(by = 'split_time'), col="line_n_split", hue = 'line', palette=line_palette,
                     col_wrap=4, height=5, col_order = order)

grid.map(sns.regplot, "split_time", "Area (microm2)", order = 3)

# Adjust the arrangement of the plots
grid.fig.tight_layout(w_pad=1)

We use the area then average all the FOV for a specific time points in each line at each split. The plot is composed by:

• a solid blue line, that is the smoothed version of this growth curve (using the function gaussian_filter1d from numpy),
• the red around that it is the standard deviation
• the dotted grey line that is the original signal

fig, ax = plt.subplots(9,5, figsize = (5*10, 7*9), gridspec_kw={'hspace': 0.7})
ax = ax.flatten().T
ax_index = 0
summary_dfs_dict = {}

for l in order:

    sub = total_df[total_df.line == l]
    sub = sub.sort_values(by = 'datetime')
    sub = sub[sub.n_split != 'day']

    splits = sub.n_split.unique().tolist()
    splits.sort()

    for split in splits:

        subsub = sub[sub.n_split == split]

        if len(subsub.split_time.unique()) > 5:
            
            ydata = subsub['Area (microm2)'].values
            xdata = subsub.split_time.values.astype('int')
    
            
            # user defined function,
            # with `area_sum` return the sum of the areas of all the field of view captured for that line at that time point
            summary_df = preprocess(subsub, original_v='Area (microm2)', final_output='mean')

            summary_dfs_dict[f'{l}_split_{split}'] = summary_df
            
            farray = np.array(summary_df['mean'])
    
            y_pos = summary_df.split_time.values
    
            # Smoothing
            farray_smooth = gaussian_filter1d(farray, sigma=3)
    
            # Error formatting
            upper_err = gaussian_filter1d(farray + (summary_df['stds'] / 2), sigma=3)
            lower_err = gaussian_filter1d(farray - (summary_df['stds'] / 2), sigma=3)
    
            ax[ax_index].scatter(xdata, ydata)
            ax[ax_index].plot(y_pos, farray, '--', linewidth=0.7, color='k', alpha=0.45)
            ax[ax_index].plot(y_pos, farray_smooth, color = '#2374AB')
            ax[ax_index].fill_between(y_pos, upper_err, lower_err, color='crimson', alpha=0.2)
            #ax[ax_index].errorbar(y_pos, farray, yerr=summary_df['stds'], fmt='none', color='crimson', alpha=0.5)
            #
            ax[ax_index].set_ylim(0, np.max(farray)+(np.max((farray)*25)/100))
            ax[ax_index].xaxis.set_tick_params(rotation=90)
            ax[ax_index].set_title(f'{l}_split_{split}')
            ax[ax_index].set_ylabel('Total area')
            ax[ax_index].set_xlabel('Time point')
            ax_index += 1
            
        else:
            print(f'Skipped split {subsub.n_split.values[0]} of line {subsub.line.values[0]}')

plt.show()

Skipped split 3 of line CTL01A
Skipped split 1 of line CTL04E
Skipped split 1 of line CTL09A
Skipped split 1 of line UCSFi001-A

Growth curves log total area

We use the logarithm of the area then sum all the FOV for a specific time points in each line at each split. The plot is composed by:

• a solid blue line, that is the smoothed version of this growth curve (using the function gaussian_filter1d from numpy),
• the red around that it is the standard deviation
• the dotted grey line that is the original signal

fig, ax = plt.subplots(10,5, figsize = (5*10, 7*9), gridspec_kw={'hspace': 0.7})
ax = ax.flatten().T
ax_index = 0

for l in order:

    sub = total_df[total_df.line == l]
    sub = sub.sort_values(by = 'datetime')
    sub = sub[sub.n_split != 'day']

    splits = sub.n_split.unique().tolist()
    splits.sort()

    for split in splits:

        subsub = sub[sub.n_split == split]

        
        # user defined function,
        # with `area_sum` return the sum of the areas of all the field of view captured for that line at that time point
        summary_df = preprocess(subsub, original_v='logArea', final_output='area_sum')
        
        farray = np.array(summary_df['area_sum'])

        y_pos = summary_df.datetime.values

        # Smoothing
        farray_smooth = gaussian_filter1d(farray, sigma=1)

        # Error formatting
        upper_err = gaussian_filter1d(farray + (summary_df['stds'] / 2), sigma=1)
        lower_err = gaussian_filter1d(farray - (summary_df['stds'] / 2), sigma=1)

        ax[ax_index].plot(y_pos, farray, '--', linewidth=0.7, color='k', alpha=0.45)
        ax[ax_index].plot(y_pos, farray_smooth, color = '#2374AB')
        ax[ax_index].fill_between(y_pos, upper_err, lower_err, color='crimson', alpha=0.2)
        #
        ax[ax_index].set_ylim(0, np.max(farray)+(np.max((farray)*25)/100))
        ax[ax_index].xaxis.set_tick_params(rotation=90)
        ax[ax_index].set_title(f'{l}_split_{split}')
        ax[ax_index].set_ylabel('Log total area')
        ax[ax_index].set_xlabel('Time point')
        ax_index += 1

plt.show()

lines = total_df.line.unique()

Discrete derivative of the curves - per line per split

We use the total area and then sum all the FOV for a specific time points in each line at each split. Then we smoothed it with gaussian_filter1d and computed the diff, corresponding to the first discrete derivative.

discrete_deriv_curves = {}

fig, ax = plt.subplots(10,5, figsize = (5*10, 7*9), gridspec_kw={'hspace': 0.7})
ax = ax.flatten().T
ax_index = 0

for l in total_df.line.unique():
    
    #color = color_dict[l]

    sub = total_df[total_df.line == l]
    sub = sub.sort_values(by = 'datetime')
    sub = sub[sub.n_split != 'day']

    for split in sub.n_split.unique():

        subsub = sub[sub.n_split == split]

        # user defined function,
        # with `area_sum` return the sum of the areas of all the field of view captured for that line at that time point
        summary_df = preprocess(subsub, original_v='Area (microm2)', final_output='mean')
        
        summary_df = summary_df.sort_values('split_time')
        
        summary_df['smoothed'] = gaussian_filter1d(summary_df['mean'], 3)
        summary_df['derivative'] = summary_df['smoothed'].diff() / summary_df['split_time'].diff()

        discrete_deriv_curves[f'{l}_split_{split}'] = summary_df
        
        farray = np.array(summary_df['derivative'])
        
        y_pos = summary_df.split_time.values
        
        ax[ax_index].errorbar(y_pos, farray, marker = 'o')
        
        ax[ax_index]

        ax[ax_index].xaxis.set_tick_params(rotation=90)
        ax[ax_index].set_title(f'{l}_split_{split}')
        ax[ax_index].set_ylabel('Discrete derivative')
        ax[ax_index].set_xlabel('Time point')
        ax_index += 1
        

plt.show()

Discrete derivative of the curves - per line

We collected the results for each line and each split and we can use it to converge to a single result for each line using as replicates the splits.

deriv_df = pd.concat(discrete_deriv_curves.values(), keys = discrete_deriv_curves.keys()).reset_index()
deriv_df['line'] = deriv_df['level_0'].apply(lambda x: x.split('_')[0])
deriv_df['split'] = deriv_df['level_0'].apply(lambda x: x.split('_')[-1])

fig, ax = plt.subplots(4,3, figsize = (5*4, 7*3), gridspec_kw={'hspace': 0.7})
ax = ax.flatten().T
ax_index = 0

for line in deriv_df.line.unique():
    
    #color = color_dict[l]

    sub = deriv_df[deriv_df.line == line]
    
    sub = sub.sort_values('split_time')

    sub['smoothed'] = gaussian_filter1d(sub['derivative'], sigma = 3)

    sns.lineplot(data = sub, y = 'smoothed', x = 'split_time', hue = 'split', ax = ax[ax_index], errorbar='sd', markers = True, palette=split_palette)
    ax[ax_index].xaxis.set_tick_params(rotation=90)
    ax[ax_index].set_title(f'{line}')
    ax[ax_index].set_ylabel('Discrete derivative')
    ax[ax_index].set_xlabel('Time point')
    ax_index += 1

fig, ax = plt.subplots(4,3, figsize = (5*4, 7*3)) #, gridspec_kw={'hspace': 0.7})
ax = ax.flatten().T
ax_index = 0

for line in deriv_df.line.unique():
    
    #color = color_dict[l]

    sub = deriv_df[deriv_df.line == line]
    
    sub = sub.sort_values('split_time')

    sub['smoothed'] = gaussian_filter1d(sub['derivative'], sigma = 3)

    sns.lineplot(data = sub, y = 'smoothed', x = 'split_time', ax = ax[ax_index], errorbar='sd', markers = True, err_style = 'bars')
    ax[ax_index].xaxis.set_tick_params(rotation=90)
    ax[ax_index].set_title(f'{line}')
    ax[ax_index].set_ylabel('Discrete derivative')
    ax[ax_index].set_xlabel('Time point')
    ax_index += 1
    
plt.tight_layout()

Cumulative of the areas - per line per split

We use the total area and then average all the FOV for a specific time points in each line at each split. Then we smoothed it with gaussian_filter1d and computed the cumulative sum over the discrete differential of the growth. with the cumsum() function.

fig, ax = plt.subplots(9,5, figsize = (5*10, 7*9))
ax = ax.flatten().T
ax_index = 0

order_line_n = total_df.line_n_split.unique().tolist()
order_line_n.sort()

for line_n in order_line_n:
    
    sub = total_df[total_df.line_n_split == line_n]
    #sub = sub[~sub.index.duplicated()]
    sub = sub.sort_values('split_time')

    if len(sub.split_time.unique()) > 5:
        
        #sub['smoothed'] = sub.groupby('line_n_split')['Area (microm2)'].apply(gaussian_filter1d, sigma = 3).loc[line_n]
        y = sub.groupby('split_time')['Area (mm2)'].mean().cumsum().values
        x = sub.split_time.unique()
        
        sns.lineplot(y = y, x = x, ax = ax[ax_index], errorbar='sd', markers = True, err_style='bars')
        ax[ax_index].xaxis.set_tick_params(rotation=90)
        ax[ax_index].set_title(f'{line_n}')
        ax[ax_index].set_ylabel('Cumulative of mean total area')
        ax[ax_index].set_xlabel('Time point')
        ax_index += 1

plt.tight_layout()

sns.set(style="white", palette="Paired", color_codes=True)
fig, ax = plt.subplots(figsize=(7,5))
labels = []
lc = []
handles = []
all_lines = {}

total_df_no_first = total_df[total_df.n_split != '1'].copy()

for l in total_df.line.unique():
    
    color = line_palette[l]

    sub = total_df[total_df.line == l]
    sub = sub.sort_values(by = 'datetime')
    sub = sub[sub.n_split != 'day']

    for split in sub.n_split.unique():

        subsub = sub[sub.n_split == split]

        # user defined function,
        # with `area_sum` return the sum of the areas of all the field of view captured for that line at that time point
        summary_df = preprocess(subsub, original_v='Area (mm2)', final_output='mean')
        
        summary_df = summary_df.sort_values('split_time')
        
        summary_df['smoothed'] = gaussian_filter1d(summary_df['mean'], 1)
        summary_df['cumulative'] = summary_df['smoothed'].cumsum()
        
        farray = np.array(summary_df['cumulative'])
        
        y_pos = summary_df.split_time.values

        line, = ax.plot(y_pos, farray, color = color, marker = '.')
        ax.xaxis.set_tick_params(rotation=90)
        all_lines[f'{l}_{split}'] = line

    labels.append(l)
    handles.append(line)
    lc.append(color)
    
plt.legend(handles, labels, bbox_to_anchor = (1,1))

<matplotlib.legend.Legend at 0x7f6c31d94310>

lines = total_df.line.unique()

highlight_growth_curves(all_lines, xlabel = 'Hours from split', ylabel = 'Cumulative growth', lines = lines, fontsize = 20)
#plt.savefig('growth_curve_per_line.pdf', dpi = 300)

fig, ax = plt.subplots(5,9, figsize = (5*12, 8*5))
ax = ax.flatten().T
ax_index = 0

fitted_param = {}

def exp_model(t, a, b):
    return a * np.exp(b * t)

for line_n in order_line_n:

    fitted_param[line_n] = {}
    sub = total_df[total_df.line_n_split == line_n]
    sub = sub.sort_values('split_time')
    
    if len(sub.split_time.unique()) > 5:
        # Calculate the cumulative sum of the mean total area for each split_time
        y = sub.groupby('split_time')['Area (mm2)'].mean().cumsum().values
        x = np.array(sub.split_time.unique())
        hue = [line_n.split('_')[0]]*len(y)

        try:
            popt, pcov = curve_fit(exp_model, x, y, p0=(max(y), 0.1))

            fitted_param[line_n]['a'] = popt[0]
            fitted_param[line_n]['rate'] = popt[1]
            fitted_param[line_n]['mean_cum'] = y
            fitted_param[line_n]['split_time'] = x
            
            a, b = popt
            
            # Generate fitted y values
            y_fitted = exp_model(x, a, b)

            fitted_param[line_n]['y_fitted'] = y_fitted
            fitted_param[line_n]['MSLE'] = mean_squared_log_error(y, y_fitted)
            fitted_param[line_n]['r2'] = r2_score(y, y_fitted)
            
            sns.lineplot(y = y_fitted, x = x, ax = ax[ax_index], markers = True, hue = hue, palette=line_palette, linewidth = 5, legend = None)
            sns.scatterplot(y = y, x = x, ax = ax[ax_index], markers = True, hue = hue, palette=line_palette, s = 150, legend=None)
            ax[ax_index].xaxis.set_tick_params(rotation=90)
            ax[ax_index].set_title(f'{line_n}', fontsize = 40)
            ax[ax_index].set_ylabel('Cumulative area (mm2)', fontsize = 35)
            ax[ax_index].set_xlabel('Time point', fontsize = 35)
            _ = ax[ax_index].set_xticklabels(ax[ax_index].get_xticklabels(), fontsize = 30)
            _ = ax[ax_index].set_yticklabels(ax[ax_index].get_yticklabels(), fontsize = 30)
            ax_index += 1
        
        except RuntimeError as e:
            print(f"Fitting failed for line_n {line_n}: {e}")
            
plt.tight_layout()
plt.savefig('./figures/Fitted_cum_area_per_split.svg', dpi = 300, bbox_inches = 'tight')

sns.set(style="white", palette="Paired", color_codes=True)
fig, ax = plt.subplots(figsize=(7,5))
labels = []
lc = []
handles = []
all_lines = {}

total_df_no_first = total_df[total_df.n_split != '1'].copy()

for l in total_df.line.unique():
    
    color = line_palette[l]

    sub = total_df[total_df.line == l]
    sub = sub.sort_values(by = 'datetime')
    sub = sub[sub.n_split != 'day']

    for split in sub.n_split.unique():


        subsub = sub[sub.n_split == split]

        if len(subsub.split_time.unique()) > 5:

            # user defined function,
            # with `area_sum` return the sum of the areas of all the field of view captured for that line at that time point
            summary_df = preprocess(subsub, original_v='Area (mm2)', final_output='mean')
            
            summary_df = summary_df.sort_values('split_time')
            summary_df['cumulative'] = summary_df['mean'].cumsum()
            
            farray = np.array(summary_df['cumulative'].values)
            y_pos = summary_df.split_time.values
    
            popt, pcov = curve_fit(exp_model, y_pos, farray, p0=(max(farray), 0.1))
            
            a, b = popt
    
            y_fitted = exp_model(y_pos, a, b)
    
            line, = ax.plot(y_pos, y_fitted, color = color, marker = '.')
            ax.xaxis.set_tick_params(rotation=90)
            all_lines[f'{l}_{split}'] = line
    
        labels.append(l)
        handles.append(line)
        lc.append(color)
    
plt.legend(handles, labels, bbox_to_anchor = (1,1))

<matplotlib.legend.Legend at 0x7f6c32173730>

lines = total_df.line.unique()

highlight_growth_curves(all_lines, xlabel = 'Hours from split', ylabel = 'Cumulative area (mm2)', lines = lines, fontsize = 20)
plt.savefig('./figures/cumulative_growth_curve_per_line.svg', dpi = 300)

fitted_df = pd.DataFrame.from_dict(fitted_param).T
fitted_df['Line'] = fitted_df.reset_index()['index'].apply(lambda x: x.split('_')[0]).values
fitted_df['split'] = fitted_df.reset_index()['index'].apply(lambda x: x.split('_')[1]).values
fitted_df = fitted_df[~fitted_df.a.isna()]
#fitted_df

fitted_df_filtered = fitted_df[fitted_df['r2'] > 0.9]
fitted_df_filtered

	a	rate	mean_cum	split_time	y_fitted	MSLE	r2	Line	split
CTL01A_2	44.192008	0.032972	[48.98585999999999, 195.08369999999996, 285.83...	[49.0, 57.0, 72.0, 81.0, 96.0, 105.0, 120.0]	[222.33018031900514, 289.43715927487756, 474.6...	0.388249	0.951651	CTL01A	2
CTL01A_4	945.527198	0.032063	[407.73135, 650.817798, 1470.892803, 2865.8591...	[0.0, 8.0, 25.0, 33.0, 48.0, 56.0, 73.0]	[945.5271977458456, 1222.0016311780946, 2107.6...	0.18731	0.936356	CTL01A	4
CTL02A_1	411.679362	0.023629	[405.32601, 534.56623, 880.29901, 1318.17853, ...	[39.0, 48.0, 63.0, 72.0, 88.0, 96.0, 111.0, 12...	[1034.6010611189106, 1279.7641959460173, 1824....	0.233463	0.971479	CTL02A	1
CTL02A_2	345.17392	0.043891	[481.00286399999993, 682.5998189999999, 1748.9...	[15.0, 24.0, 39.0, 50.0, 63.0, 72.0, 87.0, 96.0]	[666.7525349575958, 989.739028170901, 1911.821...	0.038571	0.992569	CTL02A	2
CTL02A_3	3436.282608	0.019792	[627.73808, 992.027444, 1508.292068, 2111.0835...	[0.0, 5.0, 20.0, 29.0, 44.0, 52.0, 68.0, 76.0,...	[3436.282608164845, 3793.7273295904215, 5105.0...	0.579326	0.962535	CTL02A	3
CTL02A_5	235.308712	0.039375	[248.92647, 348.61422, 667.6209999999999, 927....	[0.0, 16.0, 24.0, 39.0, 48.0, 63.0]	[235.30871162314125, 441.8201612979932, 605.40...	0.018336	0.982764	CTL02A	5
CTL04E_2	226.365471	0.02725	[114.00317999999999, 419.92985999999996, 648.0...	[24.0, 33.0, 49.0, 57.0, 72.0, 81.0, 96.0, 105...	[435.3502598087916, 556.3518577625465, 860.403...	0.222511	0.980698	CTL04E	2
CTL04E_3	539.373742	0.022668	[807.9485999999999, 925.2285899999999, 1018.98...	[15.0, 24.0, 39.0, 50.0, 63.0, 72.0, 87.0, 96....	[757.8076669846054, 929.3097891009512, 1305.65...	0.064937	0.979539	CTL04E	3
CTL04E_4	1709.286905	0.023495	[463.8341, 808.1382349999999, 1096.15610299999...	[0.0, 8.0, 25.0, 33.0, 48.0, 56.0, 73.0, 81.0,...	[1709.2869051554621, 2062.744367831728, 3075.4...	0.342903	0.97955	CTL04E	4
CTL05A_1	293.207013	0.031328	[296.48830799999996, 923.25726, 1722.042108, 2...	[39.0, 48.0, 63.0, 72.0, 88.0, 96.0, 111.0, 12...	[994.9181087589576, 1318.9747614353005, 2110.1...	0.164421	0.997846	CTL05A	1
CTL05A_2	29.454331	0.040786	[78.09385499999999, 193.287147, 241.072407, 38...	[9.0, 24.0, 33.0, 48.0, 59.0, 72.0, 81.0, 96.0...	[42.51742389389032, 78.39046649841391, 113.156...	0.188402	0.998611	CTL05A	2
CTL05A_3	735.796188	0.020412	[544.2033449999999, 640.3876889999999, 671.980...	[0.0, 15.0, 23.0, 39.0, 47.0, 64.0, 72.0, 87.0...	[735.7961876719627, 999.3719254230257, 1176.64...	0.164413	0.981179	CTL05A	3
CTL06F_1	71.504348	0.038951	[71.0148, 191.69752499999998, 376.873929, 754....	[0.0, 39.0, 48.0, 63.0, 72.0, 88.0, 96.0, 111....	[71.50434825019778, 326.6395949886104, 463.783...	0.035333	0.998462	CTL06F	1
CTL06F_2	86.83855	0.046409	[84.18644, 202.243508, 373.50316399999997, 681...	[0.0, 9.0, 24.0, 33.0, 48.0, 59.0, 72.0, 81.0,...	[86.8385498371545, 131.85924957029783, 264.509...	0.065233	0.998126	CTL06F	2
CTL06F_3	2179.790117	0.020238	[317.817864, 537.075576, 993.100164, 1955.1224...	[0.0, 5.0, 20.0, 29.0, 44.0, 52.0, 68.0, 76.0,...	[2179.7901169835372, 2411.9067318461553, 3267....	0.534267	0.985096	CTL06F	3
CTL06F_5	457.640381	0.031442	[378.69431000000003, 785.843438, 1021.701998, ...	[0.0, 16.0, 24.0, 39.0, 48.0, 63.0]	[457.64038083814654, 756.8410668189582, 973.29...	0.007437	0.995491	CTL06F	5
CTL07C_2	73.894511	0.03302	[37.458996, 104.79609599999999, 185.987292, 28...	[9.0, 24.0, 33.0, 49.0, 57.0, 72.0, 81.0, 96.0...	[99.46594192154207, 163.22177467691895, 219.70...	0.128169	0.9895	CTL07C	2
CTL07C_3	685.286497	0.034412	[913.3792199999999, 1250.2052039999999, 1652.8...	[0.0, 15.0, 24.0, 39.0, 50.0, 63.0, 72.0, 87.0]	[685.2864972375706, 1148.2787682215853, 1565.1...	0.013741	0.998142	CTL07C	3
CTL07C_4	1522.709487	0.021389	[182.26073999999997, 304.74484799999993, 570.8...	[0.0, 5.0, 20.0, 29.0, 44.0, 52.0, 68.0, 76.0,...	[1522.7094867743351, 1694.580661740262, 2335.5...	0.829412	0.972545	CTL07C	4
CTL07C_6	498.902314	0.040869	[273.1388, 520.0346, 1032.9212599999998, 2528....	[0.0, 16.0, 24.0, 39.0, 48.0, 63.0]	[498.90231351445, 959.4102068353367, 1330.4505...	0.139212	0.967463	CTL07C	6
CTL08A_1	346.700733	0.03576	[127.16147999999998, 431.94275999999996, 1240....	[0.0, 39.0, 48.0, 63.0, 72.0, 88.0, 96.0, 111.0]	[346.7007334499812, 1398.4393021645658, 1929.3...	0.328524	0.977399	CTL08A	1
CTL08A_2	231.031507	0.034296	[62.86313999999999, 162.41026799999997, 252.89...	[0.0, 15.0, 24.0, 39.0, 48.0, 63.0, 72.0, 87.0...	[231.03150707014152, 386.44678196779114, 526.1...	0.307433	0.995233	CTL08A	2
CTL08A_3	1195.731872	0.023814	[140.72618999999997, 259.12742999999995, 598.6...	[0.0, 5.0, 20.0, 29.0, 44.0, 52.0, 68.0, 76.0,...	[1195.7318723513963, 1346.931356484199, 1925.2...	0.872422	0.967654	CTL08A	3
CTL09A_2	100.290935	0.036553	[158.31083999999998, 305.1929799999999, 625.27...	[33.0, 49.0, 57.0, 72.0, 81.0, 96.0, 105.0, 12...	[335.05944132725455, 601.3324964971382, 805.58...	0.143439	0.984661	CTL09A	2
CTL09A_3	722.000766	0.031095	[416.53340399999996, 845.522964, 1353.60639600...	[15.0, 24.0, 39.0, 50.0, 63.0, 72.0, 87.0, 96....	[1151.079689056732, 1522.8110877598822, 2427.8...	0.211774	0.977202	CTL09A	3
CTL09A_4	1105.844842	0.026066	[325.85663999999997, 564.9259079999999, 1003.4...	[9.0, 24.0, 32.0, 48.0, 56.0, 73.0, 81.0, 96.0...	[1398.2275206445206, 2067.206814931102, 2546.5...	0.420498	0.988261	CTL09A	4
CTL09A_5	373.444343	0.039375	[380.20518, 567.604212, 948.6578159999999, 174...	[0.0, 8.0, 24.0, 32.0, 47.0, 56.0, 71.0]	[373.4443426152249, 511.7165300770923, 960.807...	0.015238	0.985174	CTL09A	5
H1_1	247.94659	0.02451	[48.570755999999996, 109.48395599999999, 128.7...	[9.0, 24.0, 33.0, 48.0, 57.0, 72.0, 83.0, 96.0...	[309.14170871482054, 446.50196530762344, 556.7...	0.841312	0.97756	H1	1
H1_2	1205.112667	0.015274	[940.9516199999999, 1109.298648, 1189.804168, ...	[0.0, 15.0, 39.0, 47.0, 64.0, 72.0, 87.0, 95.0...	[1205.1126672840826, 1515.405420418225, 2186.4...	0.165697	0.950816	H1	2
H9_1	929.110322	0.028899	[143.72009999999997, 367.2745799999999, 947.59...	[0.0, 15.0, 24.0, 40.0, 48.0, 63.0, 72.0, 87.0...	[929.1103223762867, 1433.277124436774, 1859.03...	0.595617	0.97611	H9	1
H9_2	209.235095	0.047362	[114.86429999999999, 704.2667159999999, 1200.7...	[15.0, 24.0, 39.0, 50.0, 63.0, 72.0, 87.0]	[425.76448866501073, 652.0642337088078, 1326.8...	0.245584	0.998409	H9	2
H9_3	2342.416999	0.018932	[344.70881999999995, 429.92740799999996, 542.4...	[0.0, 5.0, 20.0, 29.0, 44.0, 52.0, 68.0, 76.0,...	[2342.416999320976, 2574.9795323832, 3420.6015...	0.938483	0.963001	H9	3
H9_5	327.17464	0.028579	[308.090865, 343.77042, 682.5535199999999, 935...	[0.0, 16.0, 17.0, 39.0, 48.0, 63.0]	[327.1746404878582, 516.8499677508379, 531.833...	0.040654	0.963915	H9	5
KTD8.2_1	104.47087	0.03995	[209.46329999999998, 355.660845, 580.268264999...	[0.0, 39.0, 48.0, 63.0, 72.0, 88.0, 96.0, 111.0]	[104.47087006795536, 496.18993729676833, 710.8...	0.08602	0.987708	KTD8.2	1
KTD8.2_2	267.491	0.03443	[271.62816, 429.56363999999996, 1188.767879999...	[0.0, 15.0, 24.0, 39.0, 48.0, 63.0, 72.0, 87.0...	[267.4910002980408, 448.3342142395313, 611.191...	0.059554	0.983557	KTD8.2	2
KTD8.2_3	571.418893	0.020138	[40.886087999999994, 148.963548, 230.079948, 3...	[9.0, 28.0, 33.0, 48.0, 57.0, 72.0, 80.0, 96.0...	[684.9629488261039, 1004.2408456227806, 1110.6...	1.101126	0.984485	KTD8.2	3
KTD8.2_4	543.529985	0.028306	[539.3101333333333, 824.4388333333333, 1098.55...	[0.0, 16.0, 24.0, 39.0, 48.0, 63.0]	[543.5299854659438, 854.8923367343343, 1072.14...	0.003265	0.986757	KTD8.2	4
UCSFi001-A_2	196.98018	0.027632	[179.12193, 422.4456, 664.010115, 768.59238, 1...	[24.0, 33.0, 49.0, 57.0, 72.0, 81.0, 96.0, 105...	[382.3265106939781, 490.27400788144416, 762.86...	0.098251	0.969733	UCSFi001-A	2
UCSFi001-A_3	372.597267	0.026192	[313.51438, 394.810525, 511.56956499999995, 92...	[0.0, 15.0, 24.0, 39.0, 50.0, 63.0, 72.0, 87.0...	[372.5972665773523, 551.9061476057238, 698.619...	0.025112	0.99524	UCSFi001-A	3
UCSFi001-A_4	2047.342656	0.022357	[250.04633999999996, 519.1565519999999, 1278.6...	[0.0, 8.0, 25.0, 33.0, 48.0, 56.0, 73.0, 81.0,...	[2047.3426556901313, 2448.3183682685094, 3580....	0.685379	0.979739	UCSFi001-A	4
UCSFi001-A_5	343.308488	0.052116	[675.93918, 889.3241639999999, 1171.628004, 18...	[0.0, 16.0, 24.0, 39.0, 48.0, 63.0]	[343.30848825179106, 790.359528544613, 1199.20...	0.100988	0.980453	UCSFi001-A	5

fig, ax = plt.subplots()
sns.barplot(data = fitted_df_filtered, x = 'split', y = 'rate', order = ['1', '2', '3', '4', '5', '6'], ax = ax)#, hue = 'Line', palette=line_palette)
_ = ax.set_ylabel('Growth rate', fontsize = 20)
_ = ax.set_yticklabels(ax.get_yticklabels(), fontsize = 15)
_ = ax.set_xlabel('Passage', fontsize = 20)
_ = ax.set_xticklabels(ax.get_xticklabels(), fontsize = 15)

fig, ax = plt.subplots(figsize = (10,4))
fitted_df_filtered['split'] = fitted_df_filtered['split'].astype('int')
sns.lineplot(data = fitted_df_filtered, x = 'split', y = 'rate', hue = 'Line',
              ax = ax, palette=line_palette)
_ = ax.set_ylabel('Growth rate', fontsize = 20)
_ = ax.set_yticklabels(ax.get_yticklabels(), fontsize = 15)
_ = ax.set_xlabel('Passage', fontsize = 20)
_ = ax.set_xticklabels(ax.get_xticklabels(), fontsize = 15)
ax.legend(bbox_to_anchor = (1,1))

<matplotlib.legend.Legend at 0x7f6c2a74f280>

fig, ax = plt.subplots()
sns.boxplot(data = fitted_df_filtered, x = 'Line', y = 'rate', ax = ax, palette=line_palette)
_ = ax.set_ylabel('Rate of area growth', fontsize = 20)
_ = ax.set_yticklabels(ax.get_yticklabels(), fontsize = 15)
_ = ax.set_xlabel('Passage', fontsize = 20)
_ = ax.set_xticklabels(ax.get_xticklabels(), fontsize = 15, rotation = 90)

fitted_df_filtered.sort_values(by = 'rate').to_csv('../../data/csv/iPSC_fitted_exp_area_sum_per_split.csv')

fitted_df_filtered.sort_values(by = 'rate')

	a	rate	mean_cum	split_time	y_fitted	MSLE	r2	Line	split
H1_2	1205.112667	0.015274	[940.9516199999999, 1109.298648, 1189.804168, ...	[0.0, 15.0, 39.0, 47.0, 64.0, 72.0, 87.0, 95.0...	[1205.1126672840826, 1515.405420418225, 2186.4...	0.165697	0.950816	H1	2
H9_3	2342.416999	0.018932	[344.70881999999995, 429.92740799999996, 542.4...	[0.0, 5.0, 20.0, 29.0, 44.0, 52.0, 68.0, 76.0,...	[2342.416999320976, 2574.9795323832, 3420.6015...	0.938483	0.963001	H9	3
CTL02A_3	3436.282608	0.019792	[627.73808, 992.027444, 1508.292068, 2111.0835...	[0.0, 5.0, 20.0, 29.0, 44.0, 52.0, 68.0, 76.0,...	[3436.282608164845, 3793.7273295904215, 5105.0...	0.579326	0.962535	CTL02A	3
KTD8.2_3	571.418893	0.020138	[40.886087999999994, 148.963548, 230.079948, 3...	[9.0, 28.0, 33.0, 48.0, 57.0, 72.0, 80.0, 96.0...	[684.9629488261039, 1004.2408456227806, 1110.6...	1.101126	0.984485	KTD8.2	3
CTL06F_3	2179.790117	0.020238	[317.817864, 537.075576, 993.100164, 1955.1224...	[0.0, 5.0, 20.0, 29.0, 44.0, 52.0, 68.0, 76.0,...	[2179.7901169835372, 2411.9067318461553, 3267....	0.534267	0.985096	CTL06F	3
CTL05A_3	735.796188	0.020412	[544.2033449999999, 640.3876889999999, 671.980...	[0.0, 15.0, 23.0, 39.0, 47.0, 64.0, 72.0, 87.0...	[735.7961876719627, 999.3719254230257, 1176.64...	0.164413	0.981179	CTL05A	3
CTL07C_4	1522.709487	0.021389	[182.26073999999997, 304.74484799999993, 570.8...	[0.0, 5.0, 20.0, 29.0, 44.0, 52.0, 68.0, 76.0,...	[1522.7094867743351, 1694.580661740262, 2335.5...	0.829412	0.972545	CTL07C	4
UCSFi001-A_4	2047.342656	0.022357	[250.04633999999996, 519.1565519999999, 1278.6...	[0.0, 8.0, 25.0, 33.0, 48.0, 56.0, 73.0, 81.0,...	[2047.3426556901313, 2448.3183682685094, 3580....	0.685379	0.979739	UCSFi001-A	4
CTL04E_3	539.373742	0.022668	[807.9485999999999, 925.2285899999999, 1018.98...	[15.0, 24.0, 39.0, 50.0, 63.0, 72.0, 87.0, 96....	[757.8076669846054, 929.3097891009512, 1305.65...	0.064937	0.979539	CTL04E	3
CTL04E_4	1709.286905	0.023495	[463.8341, 808.1382349999999, 1096.15610299999...	[0.0, 8.0, 25.0, 33.0, 48.0, 56.0, 73.0, 81.0,...	[1709.2869051554621, 2062.744367831728, 3075.4...	0.342903	0.97955	CTL04E	4
CTL02A_1	411.679362	0.023629	[405.32601, 534.56623, 880.29901, 1318.17853, ...	[39.0, 48.0, 63.0, 72.0, 88.0, 96.0, 111.0, 12...	[1034.6010611189106, 1279.7641959460173, 1824....	0.233463	0.971479	CTL02A	1
CTL08A_3	1195.731872	0.023814	[140.72618999999997, 259.12742999999995, 598.6...	[0.0, 5.0, 20.0, 29.0, 44.0, 52.0, 68.0, 76.0,...	[1195.7318723513963, 1346.931356484199, 1925.2...	0.872422	0.967654	CTL08A	3
H1_1	247.94659	0.02451	[48.570755999999996, 109.48395599999999, 128.7...	[9.0, 24.0, 33.0, 48.0, 57.0, 72.0, 83.0, 96.0...	[309.14170871482054, 446.50196530762344, 556.7...	0.841312	0.97756	H1	1
CTL09A_4	1105.844842	0.026066	[325.85663999999997, 564.9259079999999, 1003.4...	[9.0, 24.0, 32.0, 48.0, 56.0, 73.0, 81.0, 96.0...	[1398.2275206445206, 2067.206814931102, 2546.5...	0.420498	0.988261	CTL09A	4
UCSFi001-A_3	372.597267	0.026192	[313.51438, 394.810525, 511.56956499999995, 92...	[0.0, 15.0, 24.0, 39.0, 50.0, 63.0, 72.0, 87.0...	[372.5972665773523, 551.9061476057238, 698.619...	0.025112	0.99524	UCSFi001-A	3
CTL04E_2	226.365471	0.02725	[114.00317999999999, 419.92985999999996, 648.0...	[24.0, 33.0, 49.0, 57.0, 72.0, 81.0, 96.0, 105...	[435.3502598087916, 556.3518577625465, 860.403...	0.222511	0.980698	CTL04E	2
UCSFi001-A_2	196.98018	0.027632	[179.12193, 422.4456, 664.010115, 768.59238, 1...	[24.0, 33.0, 49.0, 57.0, 72.0, 81.0, 96.0, 105...	[382.3265106939781, 490.27400788144416, 762.86...	0.098251	0.969733	UCSFi001-A	2
KTD8.2_4	543.529985	0.028306	[539.3101333333333, 824.4388333333333, 1098.55...	[0.0, 16.0, 24.0, 39.0, 48.0, 63.0]	[543.5299854659438, 854.8923367343343, 1072.14...	0.003265	0.986757	KTD8.2	4
H9_5	327.17464	0.028579	[308.090865, 343.77042, 682.5535199999999, 935...	[0.0, 16.0, 17.0, 39.0, 48.0, 63.0]	[327.1746404878582, 516.8499677508379, 531.833...	0.040654	0.963915	H9	5
H9_1	929.110322	0.028899	[143.72009999999997, 367.2745799999999, 947.59...	[0.0, 15.0, 24.0, 40.0, 48.0, 63.0, 72.0, 87.0...	[929.1103223762867, 1433.277124436774, 1859.03...	0.595617	0.97611	H9	1
CTL09A_3	722.000766	0.031095	[416.53340399999996, 845.522964, 1353.60639600...	[15.0, 24.0, 39.0, 50.0, 63.0, 72.0, 87.0, 96....	[1151.079689056732, 1522.8110877598822, 2427.8...	0.211774	0.977202	CTL09A	3
CTL05A_1	293.207013	0.031328	[296.48830799999996, 923.25726, 1722.042108, 2...	[39.0, 48.0, 63.0, 72.0, 88.0, 96.0, 111.0, 12...	[994.9181087589576, 1318.9747614353005, 2110.1...	0.164421	0.997846	CTL05A	1
CTL06F_5	457.640381	0.031442	[378.69431000000003, 785.843438, 1021.701998, ...	[0.0, 16.0, 24.0, 39.0, 48.0, 63.0]	[457.64038083814654, 756.8410668189582, 973.29...	0.007437	0.995491	CTL06F	5
CTL01A_4	945.527198	0.032063	[407.73135, 650.817798, 1470.892803, 2865.8591...	[0.0, 8.0, 25.0, 33.0, 48.0, 56.0, 73.0]	[945.5271977458456, 1222.0016311780946, 2107.6...	0.18731	0.936356	CTL01A	4
CTL01A_2	44.192008	0.032972	[48.98585999999999, 195.08369999999996, 285.83...	[49.0, 57.0, 72.0, 81.0, 96.0, 105.0, 120.0]	[222.33018031900514, 289.43715927487756, 474.6...	0.388249	0.951651	CTL01A	2
CTL07C_2	73.894511	0.03302	[37.458996, 104.79609599999999, 185.987292, 28...	[9.0, 24.0, 33.0, 49.0, 57.0, 72.0, 81.0, 96.0...	[99.46594192154207, 163.22177467691895, 219.70...	0.128169	0.9895	CTL07C	2
CTL08A_2	231.031507	0.034296	[62.86313999999999, 162.41026799999997, 252.89...	[0.0, 15.0, 24.0, 39.0, 48.0, 63.0, 72.0, 87.0...	[231.03150707014152, 386.44678196779114, 526.1...	0.307433	0.995233	CTL08A	2
CTL07C_3	685.286497	0.034412	[913.3792199999999, 1250.2052039999999, 1652.8...	[0.0, 15.0, 24.0, 39.0, 50.0, 63.0, 72.0, 87.0]	[685.2864972375706, 1148.2787682215853, 1565.1...	0.013741	0.998142	CTL07C	3
KTD8.2_2	267.491	0.03443	[271.62816, 429.56363999999996, 1188.767879999...	[0.0, 15.0, 24.0, 39.0, 48.0, 63.0, 72.0, 87.0...	[267.4910002980408, 448.3342142395313, 611.191...	0.059554	0.983557	KTD8.2	2
CTL08A_1	346.700733	0.03576	[127.16147999999998, 431.94275999999996, 1240....	[0.0, 39.0, 48.0, 63.0, 72.0, 88.0, 96.0, 111.0]	[346.7007334499812, 1398.4393021645658, 1929.3...	0.328524	0.977399	CTL08A	1
CTL09A_2	100.290935	0.036553	[158.31083999999998, 305.1929799999999, 625.27...	[33.0, 49.0, 57.0, 72.0, 81.0, 96.0, 105.0, 12...	[335.05944132725455, 601.3324964971382, 805.58...	0.143439	0.984661	CTL09A	2
CTL06F_1	71.504348	0.038951	[71.0148, 191.69752499999998, 376.873929, 754....	[0.0, 39.0, 48.0, 63.0, 72.0, 88.0, 96.0, 111....	[71.50434825019778, 326.6395949886104, 463.783...	0.035333	0.998462	CTL06F	1
CTL09A_5	373.444343	0.039375	[380.20518, 567.604212, 948.6578159999999, 174...	[0.0, 8.0, 24.0, 32.0, 47.0, 56.0, 71.0]	[373.4443426152249, 511.7165300770923, 960.807...	0.015238	0.985174	CTL09A	5
CTL02A_5	235.308712	0.039375	[248.92647, 348.61422, 667.6209999999999, 927....	[0.0, 16.0, 24.0, 39.0, 48.0, 63.0]	[235.30871162314125, 441.8201612979932, 605.40...	0.018336	0.982764	CTL02A	5
KTD8.2_1	104.47087	0.03995	[209.46329999999998, 355.660845, 580.268264999...	[0.0, 39.0, 48.0, 63.0, 72.0, 88.0, 96.0, 111.0]	[104.47087006795536, 496.18993729676833, 710.8...	0.08602	0.987708	KTD8.2	1
CTL05A_2	29.454331	0.040786	[78.09385499999999, 193.287147, 241.072407, 38...	[9.0, 24.0, 33.0, 48.0, 59.0, 72.0, 81.0, 96.0...	[42.51742389389032, 78.39046649841391, 113.156...	0.188402	0.998611	CTL05A	2
CTL07C_6	498.902314	0.040869	[273.1388, 520.0346, 1032.9212599999998, 2528....	[0.0, 16.0, 24.0, 39.0, 48.0, 63.0]	[498.90231351445, 959.4102068353367, 1330.4505...	0.139212	0.967463	CTL07C	6
CTL02A_2	345.17392	0.043891	[481.00286399999993, 682.5998189999999, 1748.9...	[15.0, 24.0, 39.0, 50.0, 63.0, 72.0, 87.0, 96.0]	[666.7525349575958, 989.739028170901, 1911.821...	0.038571	0.992569	CTL02A	2
CTL06F_2	86.83855	0.046409	[84.18644, 202.243508, 373.50316399999997, 681...	[0.0, 9.0, 24.0, 33.0, 48.0, 59.0, 72.0, 81.0,...	[86.8385498371545, 131.85924957029783, 264.509...	0.065233	0.998126	CTL06F	2
H9_2	209.235095	0.047362	[114.86429999999999, 704.2667159999999, 1200.7...	[15.0, 24.0, 39.0, 50.0, 63.0, 72.0, 87.0]	[425.76448866501073, 652.0642337088078, 1326.8...	0.245584	0.998409	H9	2
UCSFi001-A_5	343.308488	0.052116	[675.93918, 889.3241639999999, 1171.628004, 18...	[0.0, 16.0, 24.0, 39.0, 48.0, 63.0]	[343.30848825179106, 790.359528544613, 1199.20...	0.100988	0.980453	UCSFi001-A	5

pd.DataFrame(fitted_df.groupby('Line')['rate'].mean().sort_values())

	rate
Line
H1	0.019892
CTL01A	0.02909
CTL04E	0.029604
CTL08A	0.029916
KTD8.2	0.030706
CTL05A	0.030842
H9	0.030943
CTL02A	0.031672
UCSFi001-A	0.032074
CTL07C	0.032422
CTL09A	0.033272
CTL06F	0.03426

data_tot = []

for line_n in fitted_df.index:
    sub = fitted_df.loc[line_n]
    data = pd.DataFrame({'mean_cum': sub['mean_cum'], 'split_time': sub['split_time'], 'line_n': [line_n] * len(sub['mean_cum'])})
    data_tot.append(data)

data_tot = pd.concat(data_tot)

data_tot['Line'] = data_tot['line_n'].apply(lambda x: x.split('_')[0]).values
data_tot['split'] = data_tot['line_n'].apply(lambda x: x.split('_')[1]).values

fig, ax = plt.subplots(4,3, figsize = (20, 20))
ax = ax.flatten().T
ax_index = 0
fitted_param_line = {}

for line in order:

    fitted_param_line[line] = {}
    sub = data_tot[data_tot.Line == line]
    sub = sub.sort_values('split_time')
    
    if len(sub.split_time.unique()) > 5:
        # Calculate the cumulative sum of the mean total area for each split_time
        y = sub['mean_cum'].cumsum().values
        x = np.array(sub.split_time)

        try:
            popt, pcov = curve_fit(exp_model, x, y, p0=(max(y), 0.1))

            fitted_param_line[line]['intercept'] = popt[0]
            fitted_param_line[line]['rate'] = popt[1]
            fitted_param_line[line]['mean_cum'] = y
            fitted_param_line[line]['split_time'] = x
            
            a, b = popt
            
            # Generate fitted y values
            y_fitted = exp_model(x, a, b)

            fitted_param_line[line]['y_fitted'] = y_fitted
            fitted_param_line[line]['MSLE'] = mean_squared_log_error(y, y_fitted)
            fitted_param_line[line]['r2'] = r2_score(y, y_fitted)
            
            sns.lineplot(y = y_fitted, x = x, ax = ax[ax_index], markers = True)
            sns.scatterplot(y = y, x = x, ax = ax[ax_index], markers = True)
            ax[ax_index].xaxis.set_tick_params(rotation=90)
            ax[ax_index].set_title(f'{line}', fontsize = 30)
            ax[ax_index].set_ylabel('Increase in area ', fontsize = 20)
            ax[ax_index].set_xlabel('Time point', fontsize = 20)
            _ = ax[ax_index].set_xticklabels(ax[ax_index].get_xticklabels(), fontsize = 15)
            _ = ax[ax_index].set_yticklabels(ax[ax_index].get_yticklabels(), fontsize = 15)
            ax_index += 1
        
        except RuntimeError as e:
            print(f"Fitting failed for line_n {line_n}: {e}")
            
plt.tight_layout()

fitted_df_line = pd.DataFrame.from_dict(fitted_param_line).T
fitted_df_line = fitted_df_line[~fitted_df_line.intercept.isna()]
fitted_df_line.sort_values('rate')

	intercept	rate	mean_cum	split_time	y_fitted	MSLE	r2
KTD8.2	9281.067738	0.015832	[209.46329999999998, 748.7734333333333, 1020.4...	[0.0, 0.0, 0.0, 9.0, 15.0, 16.0, 24.0, 24.0, 2...	[9281.067738201718, 9281.067738201718, 9281.06...	1.173708	0.964499
CTL01A	8256.479812	0.016085	[386.42207999999994, 794.15343, 1444.971227999...	[0.0, 0.0, 8.0, 16.0, 17.0, 24.0, 25.0, 33.0, ...	[8256.479811779696, 8256.479811779696, 9390.31...	1.130135	0.805506
CTL04E	15295.49368	0.018186	[463.8341, 1094.28342, 1902.4216549999999, 271...	[0.0, 0.0, 8.0, 15.0, 16.0, 24.0, 24.0, 24.0, ...	[15295.493679955274, 15295.493679955274, 17690...	1.165687	0.927465
CTL07C	10371.622493	0.020075	[273.1388, 455.39954, 1368.77876, 1673.523608,...	[0.0, 0.0, 0.0, 5.0, 9.0, 15.0, 16.0, 20.0, 24...	[10371.62249340715, 10371.62249340715, 10371.6...	1.201451	0.983757
H9	13110.461326	0.020097	[143.72009999999997, 451.810965, 796.519785, 1...	[0.0, 0.0, 0.0, 5.0, 15.0, 15.0, 16.0, 17.0, 2...	[13110.461325598491, 13110.461325598491, 13110...	2.169899	0.95942
UCSFi001-A	12323.816373	0.0206	[313.51438, 563.56072, 1239.4998999999998, 175...	[0.0, 0.0, 0.0, 8.0, 15.0, 16.0, 24.0, 24.0, 2...	[12323.816373008252, 12323.816373008252, 12323...	1.320827	0.946282
CTL05A	5002.928069	0.022183	[544.2033449999999, 622.2971999999999, 1262.68...	[0.0, 9.0, 15.0, 23.0, 24.0, 33.0, 39.0, 39.0,...	[5002.928069044476, 6108.407285775167, 6977.99...	0.847829	0.938065
H1	2796.467958	0.022727	[940.9516199999999, 989.5223759999999, 2098.82...	[0.0, 9.0, 15.0, 24.0, 33.0, 39.0, 47.0, 48.0,...	[2796.4679575700216, 3431.171930533456, 3932.4...	0.259223	0.981416
CTL02A	11641.766203	0.023222	[627.73808, 876.66455, 1868.6919939999998, 234...	[0.0, 0.0, 5.0, 15.0, 16.0, 20.0, 24.0, 24.0, ...	[11641.766203171926, 11641.766203171926, 13075...	1.007616	0.979253
CTL06F	7817.512005	0.023313	[71.0148, 449.70911, 533.89555, 851.713414, 13...	[0.0, 0.0, 0.0, 0.0, 5.0, 9.0, 16.0, 20.0, 24....	[7817.512005475825, 7817.512005475825, 7817.51...	1.412709	0.985709
CTL08A	7258.029745	0.02409	[127.16147999999998, 400.55144, 463.41458, 604...	[0.0, 0.0, 0.0, 0.0, 5.0, 15.0, 16.0, 17.0, 20...	[7258.029744896524, 7258.029744896524, 7258.02...	1.538481	0.97063
CTL09A	7978.400332	0.024632	[380.20518, 947.8093919999999, 1273.6660319999...	[0.0, 8.0, 9.0, 15.0, 24.0, 24.0, 24.0, 32.0, ...	[7978.400331917197, 9716.224353672082, 9958.53...	0.998389	0.974265

fitted_df.r2.mean()

0.9703782325266634

fitted_df_filtered.r2.mean()

0.9803089931174649

fitted_df_line.r2.mean()

0.9513555669643324

Cumulative sum of the discrete derivative of the curves - per line per split

We use the logarithm of the area and then sum all the FOV for a specific time points in each line at each split. Then we smoothed it with gaussian_filter1d and computed the diff, corresponding to the first discrete derivative. We then use the cumsum() function to obtain the cumulative sum over the discrete differential of the growth.

fig, ax = plt.subplots(10,5, figsize = (5*10, 7*9), gridspec_kw={'hspace': 0.7})
ax = ax.flatten().T
ax_index = 0

for l in total_df.line.unique():
    
    #color = color_dict[l]

    sub = total_df[total_df.line == l]
    sub = sub.sort_values(by = 'datetime')
    sub = sub[sub.n_split != 'day']

    for split in sub.n_split.unique():

        subsub = sub[sub.n_split == split]

        
        # user defined function,
        # with `area_sum` return the sum of the areas of all the field of view captured for that line at that time point
        summary_df = preprocess(subsub, original_v='Area (microm2)', final_output='mean')
        
        summary_df = summary_df.sort_values('split_time')
        
        summary_df['smoothed'] = gaussian_filter1d(summary_df['mean'], 3)
        summary_df['derivative'] = summary_df['smoothed'].diff() / summary_df['split_time'].diff()
        summary_df['cumulative'] = summary_df['derivative'].cumsum()
        
        farray = np.array(summary_df['cumulative'])
        
        y_pos = summary_df.split_time.values
        
        ax[ax_index].errorbar(y_pos, farray, marker = 'o')

        ax[ax_index].xaxis.set_tick_params(rotation=90)
        ax[ax_index].set_title(f'{l}_split_{split}')
        ax[ax_index].set_ylabel('Cumulative growth')
        ax[ax_index].set_xlabel('Time point')
        ax_index += 1
        
plt.show()

total_df.columns

Index(['total_area', 'perc_area', 'mean_area_per_colony', 'n_colonies',
       'time_point', 'confluency/generation', 'hour', 'month', 'day', 'line',
       'datetime', 'norm_factor', 'perc_area_norm', 'err_bar_mean', 'n_split',
       'split_time', 'pixel_size', 'Area (microm2)', 'Area (mm2)',
       'line_split', 'mean_area_tp', 'area_error', 'std', 'cv', 'line_n_split',
       'logArea'],
      dtype='object')

sns.set(style="white", palette="Paired", color_codes=True)
fig, ax = plt.subplots(figsize=(7,5))
labels = []
lc = []
handles = []
all_lines = {}

total_df_no_first = total_df[total_df.n_split != '1'].copy()

cumulative_dict_dfs = {}

for l in total_df.line.unique():
    
    color = line_palette[l]

    sub = total_df[total_df.line == l]
    sub = sub.sort_values(by = 'datetime')
    sub = sub[sub.n_split != 'day']

    for split in sub.n_split.unique():


        subsub = sub[sub.n_split == split]

        if len(subsub.split_time.unique()) > 0:
    
            # user defined function,
            # with `area_sum` return the sum of the areas of all the field of view captured for that line at that time point
            summary_df = preprocess(subsub, original_v='Area (microm2)', final_output='mean')
            
            summary_df = summary_df.sort_values('split_time')
            
            summary_df['smoothed'] = gaussian_filter1d(summary_df['mean'], 3)
            summary_df['derivative'] = summary_df['smoothed'].diff() / summary_df['split_time'].diff()
            summary_df['cumulative'] = summary_df['derivative'].cumsum()
    
            cumulative_dict_dfs[f'{l}_{split}'] = summary_df
            
            farray = np.array(summary_df['cumulative'])
            
            y_pos = summary_df.split_time.values
    
            line, = ax.plot(y_pos, farray, color = color, marker = '.')
            ax.xaxis.set_tick_params(rotation=90)
            all_lines[f'{l}_{split}'] = line
    
            labels.append(l)
            handles.append(line)
            lc.append(color)
    
plt.legend(handles, labels, bbox_to_anchor = (1,1))

<matplotlib.legend.Legend at 0x7f6c28e8b400>

lines = total_df.line.unique()

highlight_growth_curves(all_lines, 
                        xlabel = 'Hours from split', 
                        ylabel = 'Cumulative growth', 
                        lines = lines, fontsize = 20)
plt.savefig('./figures/cumulative_growth_curve_per_line.svg', dpi = 300)

Fit linear model

I fit here a linear regression model taking into account all the cumulatve sums of all the splits for each line. We extrapolate the slope as the rate of growth of the line.

cumulative_df = pd.concat(cumulative_dict_dfs.values(), keys = cumulative_dict_dfs.keys()).reset_index()
cumulative_df['line'] = cumulative_df.level_0.apply(lambda x: x.split('_')[0])

cumulative_df

	level_0	level_1	time_point	mean	stds	hour	month	day	datetime	split_time	smoothed	derivative	cumulative	line
0	H1_1	0	06_11_23_t18	48570.756	30156.872900	18	11	06	2023-11-06 18:00:00	0.0	110143.004205	NaN	NaN	H1
1	H1_1	2	07_11_23_t9	60913.200	94781.769346	9	11	07	2023-11-07 09:00:00	15.0	137570.951804	1828.529840	1828.529840	H1
2	H1_1	1	07_11_23_t18	19238.925	12090.104228	18	11	07	2023-11-07 18:00:00	24.0	195181.480282	6401.169831	8229.699671	H1
3	H1_1	4	08_11_23_t9	72999.585	102548.695788	9	11	08	2023-11-08 09:00:00	39.0	287232.524109	6136.736255	14366.435926	H1
4	H1_1	3	08_11_23_t18	55094.292	61100.627807	18	11	08	2023-11-08 18:00:00	48.0	417456.373402	14469.316588	28835.752514	H1
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
459	CTL01A_5	3	20_11_23_t9	188056.464	63817.297072	9	11	20	2023-11-20 09:00:00	23.0	425051.456538	3051.706842	6177.820375	CTL01A
460	CTL01A_5	2	20_11_23_t18	633256.125	453126.246308	18	11	20	2023-11-20 18:00:00	32.0	483465.005972	6490.394382	12668.214756	CTL01A
461	CTL01A_5	5	21_11_23_t9	568493.484	354817.532310	9	11	21	2023-11-21 09:00:00	47.0	543394.794597	3995.319242	16663.533998	CTL01A
462	CTL01A_5	4	21_11_23_t17	386422.080	NaN	17	11	21	2023-11-21 17:00:00	55.0	592580.870876	6148.259535	22811.793533	CTL01A
463	CTL01A_5	6	22_11_23_t10	1151778.360	NaN	10	11	22	2023-11-22 10:00:00	72.0	620324.506463	1631.978564	24443.772097	CTL01A

464 rows × 14 columns

# Initialize a grid of plots with an Axes for each walk
grid = sns.FacetGrid(cumulative_df.sort_values(by = 'split_time'), col="line", palette=line_palette,
                     col_wrap=4, height=5)

grid.map(sns.regplot, "split_time", "cumulative", order = 1)

# Adjust the arrangement of the plots
grid.fig.tight_layout(w_pad=1)

fitted_model = {}
for l in cumulative_df.line.unique():
    
    sub = cumulative_df[cumulative_df.line == l]
    sub = sub.sort_values(by = 'datetime')

    key = f'{l}'
    fitted_model[key] = {}
    fitted_model[key]['slope'], fitted_model[key]['intercept'], fitted_model[key]['rvalue'], fitted_model[key]['pvalue'], fitted_model[key]['stderr'] = stats.linregress(sub['split_time'], sub['cumulative'].fillna(0))

fitted_model_df = pd.DataFrame.from_dict(fitted_model).T.reset_index()
fitted_model_df['line'] = fitted_model_df['index'].apply(lambda x: x.split('_')[0])
fitted_model_df.sort_values(by = 'slope')

	index	slope	intercept	rvalue	pvalue	stderr	line
11	CTL01A	644.317934	-2403.923983	0.658753	3.427561e-04	153.439932	CTL01A
0	H1	1092.216426	-17870.728308	0.929554	3.246271e-13	83.369973	H1
1	CTL04E	1957.784502	-21455.175368	0.849852	4.029196e-12	196.950623	CTL04E
3	CTL05A	2002.574201	-24668.872554	0.858594	5.454580e-12	199.285868	CTL05A
5	KTD8.2	2123.269235	-46580.571519	0.961890	3.878081e-24	95.435362	KTD8.2
10	UCSFi001-A	2410.553184	-34882.929624	0.873562	1.020601e-14	207.238467	UCSFi001-A
4	H9	3810.734488	-62725.125730	0.940884	5.551798e-19	225.539637	H9
9	CTL07C	4069.466071	-98092.360468	0.872476	2.224665e-13	369.740303	CTL07C
8	CTL08A	4263.987240	-102963.382905	0.888082	9.120149e-16	340.563762	CTL08A
7	CTL06F	4575.687405	-109378.476161	0.905129	3.365469e-17	331.626382	CTL06F
6	CTL09A	5028.233033	-88363.366680	0.895983	1.307039e-14	409.717545	CTL09A
2	CTL02A	5231.682227	-91740.048754	0.858920	1.340509e-12	506.011614	CTL02A

fitted_model_df.rvalue.mean()

0.8744732639082722

fitted_model_df.sort_values(by = 'slope').to_csv('../../data/csv/iPSC_fitted_lm_grouped.csv')